Intellectual Merit: The health of each human being is critically dependent on its particular immune system. The adaptive component of the immune system is the means by which the body learns to recognize pathogens. Deficiencies in adaptive immunity place the individual as well as the population at risk for infectious diseases and cancers. The currently available mathematical and computational tools are not yet ready to characterize the full collection of changes in the antibody-mediated adaptive immune system occurring in response to exposure to new pathogenic entities. In particular, state-of-the-art methods are hindered by only focusing on a small subset of the immune cells at a time, using simple models of immune cell maturation that are not derived from data, and only giving point estimates for parameters of those models. The investigators propose to address these limitations by developing a novel approach to high throughput sequencing data from antibody genes by developing: 1) the first fully Bayesian inferential approach to immune cell maturation; 2) the first comprehensive statistical model of antibody cell maturation and evolution, including sequence models of antibody somatic hypermutation inferred directly from data; 3) innovative inferential tools to obtain posterior distributions on the joint assignment of collections of itemsto discrete parameters - scalable computational implementations of these models and inferential frameworks leading to their widespread application. In short, our work will both develop much needed analytical methods for a recently developed type of data and open a new area of statistical research. Broader Impacts: Comprehensive statistical modeling and inference of high throughput sequencing of immune cell receptors will provide information needed for rational vaccine design, prediction of susceptibility to infections, and understanding of the pathogenesis of immune cell cancers. B cell lineage reconstructions will allow scientists to track the changes that happen to an antibody in response to pathogen evolution, enabling vaccines to stay one step ahead of pathogens. An extension of this approach will be to use these tools to characterize not only the immunity of individuals, but also of populations, for example in their ability to resist epidemics. Our formalization will motivate research on a new type of inference problem with challenging statistical aspects. Our methods will be implemented in open-source software, so that any immunology lab or clinic can use these new approaches. Moreover, the proposed statistical methodology should find other applications beyond immunology, for example, in metagenomics.